Category: Limits

Question Number 122835 by liberty last updated on 20/Nov/20 $$\underset{x\to 0}{\lim }\frac{1}{x}(\frac{1}{\sin x}-\frac{3}{\sin 3x})=?$$ Answered by $@y@mlastupdatedon20/Nov/20$$\underset{x\to 0}{\lim }\frac{1}{x}\left(\frac{\sin 3x-3\sin x}{\sin x.\sin 3x}\right)$$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}}\:\left(\frac{−\mathrm{4sin}\:^{\mathrm{3}}…

Question Number 122824 by bemath last updated on 19/Nov/20 $$\underset{x\to 0}{\lim }\frac{\sin (1-\cos x)}{2x^2}=?$$ Commented by bobhans last updated on 20/Nov/20 $$\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}{x}\right)\right)}{\mathrm{2}{x}^{\mathrm{2}} }…

Question Number 122730 by bemath last updated on 19/Nov/20 $$Givenf\left(x\right)=\cos \left(\frac{1}{x}\right)andg\left(x\right)=\tan 2x.$$$$Findtheintersectpointvertical$$$$asymptotef\left(x\right)andhorizontal$$$$asymptoteg\left(x\right)for0⩽x⩽\pi .$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 122725 by liberty last updated on 19/Nov/20 $$Findtheconstantsaandbfromthe$$$$condition:$$$$\left(i\right)\underset{x\to \mathrm{\infty }}{\lim }(\frac{x^2+1}{x+1}-ax-b)=0$$$$\left(ii\right)\underset{x\to \mathrm{\infty }}{\lim }(\sqrt{x^2-x+1}-ax-b)=0$$ Commented by Dwaipayan…

Question Number 122721 by bemath last updated on 19/Nov/20 $$\underset{x\to 1}{\lim }{\left(\frac{1+x}{2+x}\right)}^{\frac{1-\sqrt{x}}{1-x}}=?$$ Answered by Dwaipayan Shikari last updated on 19/Nov/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\frac{\mathrm{1}+{x}}{\mathrm{2}+{x}}\right)^{\frac{\mathrm{1}−\sqrt{{x}}}{\left(\mathrm{1}+\sqrt{{x}}\right)\left(\mathrm{1}−\sqrt{{x}}\right)}} \…